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Izvestiya: Mathematics, 2013, Volume 77, Issue 4, Pages 714–741
DOI: https://doi.org/10.1070/IM2013v077n04ABEH002658 (Mi im8013) 		 
This article is cited in 4 scientific papers (total in 4 papers)

The unramified two-dimensional Langlands correspondence

D. V. Osipov

Steklov Mathematical Institute of the Russian Academy of Sciences
English version PDF (475 kB) Citations (4)
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DOI: https://doi.org/10.1070/IM2013v077n04ABEH002658
Abstract: We describe the unramified Langlands correspondence for two-dimensional local fields and construct a categorical analogue of the unramified principal series representation and study its properties. The main tool for this description is the construction of a certain central extension. For this and other central extensions, we prove non-commutative reciprocity laws (that is, splitting of the central extensions over certain subgroups) for arithmetic surfaces and projective surfaces over finite fields. These reciprocity laws connect central extensions constructed locally and globally.
Keywords: 2-vector spaces, two-dimensional local fields, higher adèles, generalized Langlands programme, two-dimensional non-commutative reciprocity laws.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00145-а
11-01-12098-офи-м-2011
12-01-33024 мол_а_вед
Ministry of Education and Science of the Russian Federation НШ-5139.2012.1
Received: 22.06.2012
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2013, Volume 77, Issue 4, Pages 73–102
DOI: https://doi.org/10.4213/im8013
Bibliographic databases:
Document Type: Article
UDC: 512.75+512.585
MSC: 11R37, 14J20, 18D05
Language: English
Original paper language: Russian
Citation: D. V. Osipov, “The unramified two-dimensional Langlands correspondence”, Izv. RAN. Ser. Mat., 77:4 (2013), 73–102; Izv. Math., 77:4 (2013), 714–741
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v77/i4/p73
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:719
    Russian version PDF:226
    English version PDF:14
    References:62
    First page:30
     
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